Method and apparatus to compensate for nonlinear echo in an output of a current source

ABSTRACT

A compensator generating a compensation signal to compensate for nonlinear echo in an output of a current source. The nonlinear echo is a result of transitioning the current source between an ON state and an OFF state. The compensator includes driving, weighting, function, and compensating circuits. The driving circuit receives a first signal that is based on the output of the current source. The weighting circuit is configured to generate a second signal based on weighted versions of the first signal. The function circuit, based on the second signal, (i) updates each of multiple functions, and (ii) selects a first function. The driving circuit generates a driving signal based on the first function selected by the function circuit. The compensating circuit generates the compensation signal based on the driving signal to compensate for the nonlinear echo provided by the output of the current source.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present disclosure is a continuation Application of U.S. patent application Ser. No. 12/215,222 (now U.S. Pat. No. 8,743,939), filed on Jun. 26, 2008, which is a continuation Application of U.S. patent application Ser. No. 10/189,321 (now U.S. Pat. No. 7,409,057), filed Jul. 3, 2002. The entire disclosures of the applications referenced above are incorporated herein by reference.

FIELD

The present disclosure relates to transmitting and receiving electrical signals through a communications channel, and more particularly to a nonlinear echo compensator for a Class B transmitter line driver.

BACKGROUND

IEEE section 802.3ab, which is hereby incorporated by reference, specifies physical layer parameters for 1000 BaseT (gigabit) communications channels. The gigabit communications channel employs four twisted pairs of cable. Signals transmitted over the cable are degraded by signal attenuation, return loss, echo, and crosstalk.

Referring now to FIG. 1, a gigabit Ethernet communications channel 10 is shown. The communications channel 10 includes two nodes 12 and 14 that transmit and receive one gigabit per second (Gbps). The node 12 includes transceivers 16-1, 16-2, 16-3, and 16-4 and the node 14 includes transceivers 18-1, 18-2, 18-3 and 18-4. Each transceiver transmits at 250 Mbps. The transceivers 16 and 18 are connected to opposite ends of twisted pairs 20-1, 20-2, 20-3, and 20-4. For example, the transceiver 16-1 is connected to one end of the twisted pair 20-1. The transceiver 18-1 is connected to the opposite end of the twisted pair 20-1. Each transceiver 16 and 18 includes a transmitter 24, a receiver 26, and a hybrid circuit 28.

The transmitter 24 of the transceiver 16-1 generates a five level pulse amplitude modulated (PAM-5) signal that is transmitted by the transmitter 24 and the hybrid circuit 28 of the transceiver 16-1 onto the twisted pair 20. The hybrid circuit 28 and the receiver 26 of the transceiver 18-1 receive the PAM-5 signal. The hybrid circuit 28 enables bi-directional transmission over the same twisted pairs by filtering out the transmit signal at the receiver 26.

Attenuation refers to signal loss of the twisted pair between the transmitter of one receiver and the receiver of another transceiver and is caused by several factors including skin effect. To minimize the effect of attenuation, the lowest possible frequency range that supports the required data rate is typically used. Return loss quantifies the amount of power that is reflected due to cable impedance mismatches.

Echo occurs when signals are transmitted and received on the same twisted pair. Echo is caused by residual transmit signals and cable return loss. Crosstalk occurs due to signal coupling between twisted pairs that are in close proximity. For example, the twisted pairs used in 1000 BaseT are affected by crosstalk from adjacent twisted pairs. Near end crosstalk (NEXT) is crosstalk at the transmitter end of the twisted pair. Far-and crosstalk (FEXT) is crosstalk at the receiver end of the twisted pair. Crosstalk is preferably minimized to improve receiver symbol recovery.

Referring now to FIG. 2, the transceiver 16 includes a transmitter line driver 50 that receives a transmitter signal 52. The transmitter line driver 50 outputs a multi-level signal to a load such as a matched resistor 54. A transformer 58 couples the transceiver 16 to a twisted pair 60. A replica signal generator 64 outputs a replica of the transmitter signal 52 to a summer 66. A received signal 68 is also input to the summer 66.

Since the communications channel transmits and receives on the same twisted pair 60, the replica transmitted signal is cancelled or subtracted from the received signal 68. In addition, compensation for NEXT and echo is performed. An output of the summer 66 is input to an optional low pass filter (LPF) 70. An output of the LPF 70 is input to an analog to digital converter (ADC) 74. An output of the ADC 74 is input to a summer 78. A linear echo compensation circuit 82 and NEXT compensation circuit 83 (for NEXT₁₂, NEXT₁₃, and NEXT₁₄) are also input to the summer 78. A signal (TA_(comp)) with NEXT and linear echo compensation is output by the summer 78. Additional details concerning the transceiver 16 can be found in “Active Resistive Summer for a Transformer Hybrid”, U.S. patent application Ser. No. 09/920,240, filed Aug. 1, 2001, and “A Method and Apparatus for Digital Near-End Echo/Near-End Crosstalk Cancellation with Adaptive Correlation”, U.S. patent application Ser. No. 09/465,228, filed Dec. 17, 1999, which are hereby incorporated by reference.

Referring now to FIG. 3, the transmitter line driver 50 is shown further and typically includes a plurality of positive current cells 84 and negative current cells 86. A transmitter driver control 88 selectively switches the positive and negative current cells 84 and 86 on and off to produce positive and negative signal levels. For example, the transmitter line driver for 1000 BaseT employs five symbol levels −2, −1, 0, +1, and +2, which are usually implemented as 0V, +/−0.5V and +/−1V. Future communications systems may include additional symbol levels for increased bandwidth. For example, future signal levels may include 0, +/−2, +/−4, +/−6, and +/−8 signal levels.

Referring now to FIG. 4, a conceptual illustration of the transmitter line driver 50 is shown. The positive current cells 84 can be thought of as a plurality of individual current sources 90-1, 90-2, 90-3, . . . , and 90-n that are switched by switches SW_(P1), SW_(P2), SW_(P3), . . . , and SW_(Pn). The negative current cells 86 can be thought of a plurality of individual current sources 92-1, 92-2, 92-3, . . . , and 92-m that are switched by switches SW_(N1), SW_(N2), SW_(N3), . . . , and SW_(Nm). Typically, m=n. Referring now to FIG. 5, an exemplary positive current cell 96 is shown. In FIG. 6, an exemplary negative current cell 98 is shown. As can be appreciated, other positive and negative current cells can be utilized.

When the transmitter line driver 50 is operated in a Class A operating mode, the number of positive current cells that are turned on/off for a transition from a first signal level to a second signal level is equal to the number of negative current cells that are turned off/on. When the transmitter line driver 50 is operated in a Class B operating mode, the number of positive current cells that are turned on/off for a transition from a first signal level to a second signal level is not equal to the number of negative current cells that are turned off/on. The advantage of Class B operation is reduced power consumption as compared with Class A operation.

Referring now to FIG. 7, Class A operation of the positive and negative current cells 84 and 86 for nine symbol levels is shown. As can be appreciated, when switching between signal level 6 and signal level −4, there are an equal number of positive and negative current cells being turned on and off. In particular, five positive current cells are being turned off and five negative current cells are being turned on.

Referring now to FIG. 8, exemplary Class B operation of the positive and negative current cells 84 and 86 is shown. As can be appreciated, when switching between signal level 6 and signal level −4, an unequal number of positive and negative current cells are turned on and off. In particular, six positive current cells are turned off and four negative current cells are turned on. While Class B operation provides reduced power consumption, the asymmetry of Class B operation causes nonlinear echo that degrades performance.

SUMMARY

A nonlinear echo compensator according to the present invention compensates for nonlinear echo in a transceiver including a transmitter line driver with current cells that are operated in an asymmetric low power mode. A mapping circuit generates a pattern dependent driving signal. A canceling circuit communicates with the mapping circuit and compensates for nonlinear echo in a received signal based on the pattern dependent driving signal.

In other features, the mapping circuit receives a multi-level signal and maps the multi-level signal to the pattern dependent driving signal. The mapping circuit includes a symbol weighting circuit that generates a weighted signal. The symbol weighting circuit generates the weighted signal by summing a first product of a current symbol and a first weighting factor with a second product of a prior symbol and a second weighting factor. The mapping circuit includes a function generator that generates the pattern dependent driving signal based on the weighted signal and a scaling circuit that scales the pattern dependent driving signal.

In still other features, a coefficient generator generates a first compensator coefficient based on a sum of a prior compensator coefficient and a product of an error signal and a sign function of the pattern dependent driving signal. The coefficient generator generates first, second and third compensator coefficients.

In other features, the canceling circuit includes a first multiplier that has a first input that receives the pattern driving signal and a second input that receives the first compensator coefficient. The first multiplier generates a first product. A second multiplier has a first input that receives the pattern driving signal and a second input that receives the second compensator coefficient. The second multiplier generates a second product. A third multiplier has a first input that receives the pattern driving signal and a second input that receives the third compensator coefficient. The third multiplier generates a third product.

In still other features, the canceling circuit further includes a first unit delay that receives the third product of the third multiplier. A first summer has a first input that receives the second product of the second multiplier and a second input that communicates with the first unit delay. A second unit delay communicates with an output of the first summer. A second summer has a first input that communicates with the second unit delay and a second input that receives the first product of the first multiplier.

Further areas of applicability will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples are intended for purposes of illustration only and are not intended to be limiting.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will become more fully understood from the detailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram illustrating an exemplary gigabit communications channel according to the prior art;

FIG. 2 is a functional block diagram illustrating a transceiver with a transmitter line driver and linear echo, NEXT and replica transmitter signal compensation according to the prior art;

FIG. 3 is a functional block diagram of the transmitter line driver of FIG. 2 according to the prior art;

FIG. 4 is a conceptual electrical schematic of the transmitter line driver according to the prior art;

FIG. 5 is an electrical schematic of an exemplary positive current cell in the transmitter line driver according to the prior art;

FIG. 6 is an electrical schematic of an exemplary negative current cell in the transmitter line driver according to the prior art;

FIG. 7 is a table illustrating Class A operation of the transmitter line driver according to the prior art;

FIG. 8 is a table illustrating Class B operation of the transmitter line driver according to the prior art;

FIG. 9 illustrates ideal current cell rise and fall transition characteristics;

FIG. 10 illustrates actual current cell rise and fall transition characteristics;

FIG. 11 is a functional block diagram illustrating a transceiver with a transmitter line driver and linear and nonlinear echo, NEXT and transmitter signal compensation according to the present disclosure;

FIG. 12 illustrates a nonlinear echo compensation circuit according to the present disclosure;

FIG. 13 illustrates a mapping circuit of FIG. 12 in further detail;

FIG. 14 illustrates a least means squared (LMS) circuit according to the present disclosure; and

FIG. 15 illustrates mean squared error (MSE) as a function of sample phase for a first transceiver with linear echo compensation and a second transceiver according to the present disclosure with linear and nonlinear echo compensation.

DETAILED DESCRIPTION

The following description and is in no way intended to limiting. For purposes of clarity, the same reference numerals will be used in the drawings to identify similar elements.

Referring now to FIG. 9, rise h_(r) and fall h_(f) characteristics of an ideal current cell is shown. As can be appreciated, the ideal rise h_(r) and fall h_(f) characteristics are symmetric such that h_(r)+h_(f)=1. In FIG. 10, rise h_(r) and fall h_(f) characteristics of typical current cells are not ideal. For some time periods, h_(r)+h_(f)≠1. The nonlinear echo compensation circuit for the Class B driver according to the present disclosure compensates for nonlinear echo that is introduced as a result of this asymmetry. The transmitter line driver of the transceiver according to the present disclosure can be operated in the Class B mode with reduced power consumption and without sacrificing performance.

The sampling point of the ADC 74 is determined by the received signal and not by the transmitted signal. In some cases, the sampling point occurs when the difference between h_(r) and 1−h_(f) is greater than zero. The replica transmitter signal does not have nonlinear echo characteristics because the replica transmitter signal is not generated by the transmitter line driver, which is the source of the nonlinear echo.

Referring now to FIG. 11, a transceiver 100 according to the present disclosure receives a transmitter signal 52. The transmitter line driver 50 supplies a multi-level signal to a load such as the matched resistor 54 based on the transmitter signal 52. The transformer 58 couples the transmitter line driver 50 to the twisted pair 60. The replica signal generator 64 outputs a replica of the transmitter signal 52 to the summer 66. The received signal 68 is also input to the summer 66.

The output of the summer 66 is input to the LPF 70. An output of the LPF is input to the ADC 74. The output of the ADC 74 is input to the summer 78. The linear echo compensation signal from the linear echo compensation circuit 82 and the NEXT compensation signal from the circuit 83 (canceling NEXT₁₂, NEXT₁₃, and NEXT₁₄) are also input to the summer 78. A non-linear echo compensation signal from a compensator 104 according to the present disclosure is also input to the summer 78. A signal (TA_(comp)) with linear and nonlinear echo compensation and NEXT compensation is output by the summer 78.

Referring now to FIG. 12, the nonlinear echo compensator 104 is shown to include a mapping circuit 114 and a canceller circuit 118. A transmitted signal TA₁(k+L) is input to a variable delay 120 that provides a delay of L clock cycles. The delayed transmitter signal is input to the linear echo compensation circuit 82 and the mapping circuit 114. The mapping circuit 114 outputs a pattern dependent driving signal δ_(k) to the canceller circuit 118. The pattern dependent driving signal is input to first inputs of first, second and third multipliers 122, 124 and 126. Another input of the multiplier 122 receives a third compensator coefficient h₂ from unit delay 130. As can be appreciated, unit delays can be implemented as a register or in any other suitable manner. A second input of the multiplier 124 receives a second compensator coefficient h₁ from unit delay 132. A second input of the multiplier 126 receives a first compensator coefficient h₀ from unit delay 134.

An output of the multiplier 122 is input to unit delay 140. An output of the unit delay 140 is input to a first input of a summer 142. An output of the multiplier 124 is input to a second input of the summer 142. An output of the summer 142 is input to unit delay 146. An output of the unit delay 146 is input to a first input of a summer 148. An output of the multiplier 126 is input to a second input of the summer 148. An output of the summer 148 is input to unit delay 150. An output of the unit delay 150 is input to a summer 154.

An output of the linear echo compensation circuit 82 is input to unit delay 158. An output of the unit delay 158 is input to the summer 154. Transmitter signals from other twisted pairs are input to variable delay circuits 160, 162 and 164. Outputs of the variable delay circuits 160, 162 and 164 are input to NEXT compensation circuits 166 168 and 170. Outputs of the NEXT compensation circuits 166, 168 and 170 are summed by a summer 174 and input to the summer 154. The transmitter signal TA₁(k) is input to ADC 180 and output to a summer 184. An output of the summer 154 is input to an inverting input of the summer 184, which outputs the compensated signal (TA_(comp)) 186.

Referring now to FIG. 13, the mapping circuit 114 is illustrated in further detail. The mapping circuit 114 includes a weighting circuit 201. The transmitter signal is input to unit delay 202 and a first input of the multiplier 204. A second input of the multiplier 204 receives a first constant scale factor. An output of the unit delay 200 is input to a first input of a multiplier 208. A second input of the multiplier 208 is connected to a second constant scale factor. Outputs of the multipliers 204 and 208 are input to a summer 212. An output of the summer 212 is input to unit delay 216, which outputs a signal b_(k+1) to a function generator 220. The function generator 220 outputs the pattern dependent driving signal (before delay and scaling) as follows: δ_(k+1) =|b _(k+1) |−|b _(k)| if b _(k+1) ≧b _(k) δ_(k+1) =|b _(k) |−|b _(k+1)| if b _(k+1) <b _(k)

The pattern dependent driving signal that is output by the function generator 220 is input to unit delay 224. An output of the unit delay 224 is input to a scaling circuit 228. One exemplary scaling circuit 228 includes a multiplier 230 having a first input coupled to the unit delay 224 and a second input coupled to a constant value. The scaling circuit 228 preferably offsets the effects of the weighting circuit 201, although other scaling may be performed. In the exemplary weighting circuit 201, the signal TA₁(k) is multiplied by 6 and the signal TA₁(k−1) is multiplied by 2. The scaling circuit 228 multiplies by ⅛.

Referring now to FIG. 14, a least mean squared (LMS) circuit 250 is illustrated. The LMS circuit 250 includes a compensator coefficient generator 254. An error signal 255 is input to a selector switch 256. A receiver error signal 258 is also input to the selector switch 256. The selector switch 256 selects one of the error signals 255 or 258. The switch 256 preferably selects the output of the compensator (the summer 78 in FIG. 11) as the error signal when a remote transceiver has not sent signals. Ideally, the output of the summer 78 is zero since the receiver should not detect a signal. When an incoming signal is received, the switch 256 selects the error signal at the output of the followed detector, which eliminates the effect of the incoming signal in the error signal.

An output of the selector switch 256 is input to a multiplier 260. Another input of the multiplier 260 is coupled to a scaling factor or loop gain (μ). An output of the multiplier 260 is input to the compensator coefficient generator 254. A sign function of the transmitted signal is input to a variable delay 264. An output of the variable delay is input to a multiplier 266. An output of the multiplier 260 is input to the multiplier 266. An output of the multiplier 266 is input to a summer 270. An output of the summer 270 is fed back through a unit delay 274 to the summer 270. An output of the summer 270 is input to unit delay 276. An output of the unit delay 276 provides a linear echo compensation signal (AA₀).

A sign function of the pattern dependent driving signal is input to a variable delay 280 of the compensator coefficient generator 254. An output of the variable delay 280 is input to a multiplier 282. An output of the multiplier 260 is also input to the multiplier 282. An output of the multiplier 282 is input to a summer 284. An output of the summer 284 is input to a limiter 286, which limits the signal input between upper and lower limits. For example, the limiter 286 may limit the signal to +/− 1/32. An output of the limiter 286 is input to unit delay 288 and to unit delay 290. An output of the unit delay 290 is input to the summer 284. An output of the unit delay 288 provides the first compensator coefficient h₀ as follows: h ₀ ←h ₀ +μ*e _(k−L)*sign(δ_(k))

An output of the variable delay 280 is input to unit delay 300. An output of the unit delay 300 is input to a multiplier 302 and unit delay 304. An output of the multiplier 260 is also input to the multiplier 302. An output of the multiplier 302 is input to a summer 306. An output of the summer 306 is input to a limiter 308. An output of the limiter 308 is input to unit delays 310 and 312. An output of the unit delay 312 is input to the summer 306. An output of the unit delay 310 provides the second compensator coefficient h₁ as follows: h ₁ ←h ₁ +μ*e _(k−L)*sign(δ_(k−1))

An output of the unit delay 304 is input to a multiplier 320. An output of the multiplier 260 is also input to the multiplier 320. An output of the multiplier 320 is input to a summer 322. An output of the summer 322 is input to a limiter 324. An output of the limiter 324 is input to unit delays 326 and 328. An output of the unit delay 328 is input to the summer 322. An output of the unit delay 326 provides the third compensator coefficient h₂ as follows: h ₂ ←h ₂ +μ*e _(k−L)*sign(δ_(k−2))

Referring now to FIG. 15, mean squared error is shown as a function of sample phase. The mean squared error for transceivers with linear and nonlinear echo compensation according to the present disclosure is significantly lower than the mean squared error for transceivers with linear echo compensation.

Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present disclosure can be implemented in a variety of forms. Therefore, while the embodiments disclosed herein have been described in connection with particular examples thereof, other modifications will become apparent to the skilled practitioner upon a study of the drawings, the specification and the following claims. 

What is claimed is:
 1. A compensator configured to generate a first compensation signal to compensate for nonlinear echo in an output of a current source, wherein the nonlinear echo is a result of transitioning the current source between an ON state and an OFF state, the compensator comprising: a driving circuit configured to receive a first signal that is based on the output of the current source, wherein the first signal comprises the nonlinear echo; a weighting circuit configured to generate a second signal based on weighted versions of the first signal; a function circuit configured to, based on the second signal, (i) update each of two functions, and (ii) select a first function of the two updated functions, wherein the driving circuit is configured to generate a driving signal based on the first function selected by the function circuit; and a compensating circuit configured to generate the first compensation signal based on the driving signal to compensate for the nonlinear echo provided by the output of the current source.
 2. The compensator of claim 1, wherein: the second signal includes a first symbol and a second symbol; and the function circuit is configured to select the first function of the two updated functions based on a relationship between the first symbol and the second symbol.
 3. The compensator of claim 1, wherein: the second signal includes a symbol; and each of the two updated functions includes the symbol.
 4. The compensator of claim 1, wherein the weighting circuit is configured to generate the second signal by summing (i) a first product of a first weighting factor and the first signal with (ii) a second product of a second weighting factor and a delayed version of the first signal.
 5. The compensator of claim 1, further comprising a scaling circuit configured to scale an output of the function circuit to provide the driving signal.
 6. The compensator of claim 1, further comprising a coefficient generator configured to generate a plurality of coefficients, wherein the compensating circuit is configured to generate the first compensation signal based on the plurality of coefficients.
 7. The compensator of claim 6, wherein: the plurality of coefficients comprise a first coefficient and a second coefficient; and the compensating circuit comprises: a first multiplier configured to generate a first product based on (i) the driving signal, and (ii) the first coefficient, and a second multiplier configured to generate a second product based on (i) the driving signal, and (ii) the second coefficient, wherein the compensating circuit is configured to generate the first compensation signal based on the first product and the second product.
 8. The compensator of claim 7, wherein the compensating circuit comprises: a delay circuit configured to receive the first product; and a first summer configured to sum (i) an output of the delay circuit, and (ii) the second product, wherein the compensating circuit is configured to generate the first compensation signal based on an output of the first summer.
 9. A system comprising: the compensator of claim 1; a second compensator configured to generate a second compensation signal to compensate for linear echo in the first signal; a first summer configured to generate a combined signal based on the first compensation signal and the second compensation signal; and a second summer configured to generate a compensated signal based on (i) the first signal received by the driving circuit, and (ii) the combined signal.
 10. The system of claim 9, further comprising a crosstalk signal generator configured to generate a crosstalk signal, wherein: the first signal is transmitted on a first twisted pair cable; the crosstalk signal is indicative of crosstalk experienced on the first twisted pair cable due to transmission of a third signal on a second twisted pair cable; and the first summer is configured to generate the combined signal based on the crosstalk signal.
 11. A method of compensating for nonlinear echo in an output of a current source including generating a first compensation signal, wherein the nonlinear echo is a result of transitioning the current source between an ON state and an OFF state, the method comprising: receiving a first signal that is based on the output of the current source, wherein the first signal comprises the nonlinear echo; generating a second signal based on weighted versions of the first signal; based on the second signal, (i) updating each of two functions, and (ii) selecting a first function of the two updated functions; generating a driving signal based on the selected first function; and generating the first compensation signal based on the driving signal to compensate for the nonlinear echo provided by the output of the current source.
 12. The method of claim 11, comprising selecting the first function of the two updated functions based on a relationship between a first symbol and a second symbol, wherein the second signal includes the first symbol and the second symbol.
 13. The method of claim 11, wherein: the second signal includes a symbol; and each of the two updated functions includes the symbol.
 14. The method of claim 11, comprising generating the second signal by summing (i) a first product of a first weighting factor and the first signal with (ii) a second product of a second weighting factor and a delayed version of the first signal.
 15. The method of claim 11, further comprising scaling an output of a function circuit to provide the driving signal, wherein the first function of the two updated functions is selected by the function circuit.
 16. The method of claim 11, further comprising generating a plurality of coefficients, wherein the first compensation signal is generated based on the plurality of coefficients.
 17. The method of claim 16, further comprising: generating a first product based on (i) the driving signal, and (ii) a first coefficient, wherein the plurality of coefficients comprise the first coefficient and a second coefficient; and generating a second product based on (i) the driving signal, and (ii) the second coefficient, wherein the first compensation signal is generated based on the first product and the second product.
 18. The method of claim 17, further comprising: receiving the first product at a delay circuit; and summing the second product and an output of the delay circuit to generate a sum, wherein the first compensation signal is generated based on the sum.
 19. The method of claim 11, further comprising: generating a second compensation signal to compensate for linear echo in the first signal; generating a combined signal based on the first compensation signal and the second compensation signal; and generating a compensated signal based on (i) the first signal received based on the output of the current source, and (ii) the combined signal.
 20. The method of claim 19, further comprising generating a crosstalk signal, wherein: the first signal is transmitted on a first twisted pair cable; the crosstalk signal is indicative of crosstalk experienced on the first twisted pair cable due to transmission of a third signal on a second twisted pair cable; and the combined signal is generated based on the crosstalk signal. 